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01. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is: 
A. 2 : 3 B. 3 : 2
C. 3 : 4 D. 4 : 3

Answer and Explanation

Answer: 3 : 4

Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.

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02. A car travelling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car. 
A. 17 6/7 km/hr B. 25 km/hr
C. 30 km/hr D. 35 km/hr

Answer and Explanation

Answer: 35 km/hr

Explanation:
Time taken = 1 hr 40 min 48 sec = 1 hr 40 4/5 min = 1 51/75 hrs = 126/75 hrs.

Let the actual speed be x km/hr.
Then, 5/7 x * 126/75 = 42

x = (42 x 7 x 75) / (5 x 126 )   = 35 km/hr.
 

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03. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. 
A. 220 km B. 224 km
C. 230 km D. 234 km

Answer and Explanation

Answer: 224 km

Explanation:

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04. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is: 
A. 100 kmph B. 110 kmph
C. 120 kmph D. 130 kmph

Answer and Explanation

Answer: 120 kmph

Explanation:

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05. A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?
A. 47.5 B. 50
C.  45 D. 40

Answer and Explanation

Answer: 40

Explanation:
The average speed ‘v’, when a man travels two same distance with different speeds ‘v1’ and ‘v2’ is:
v = (2*v1*v2) / (v1 + v2)
In the above problem, v1 = 30 and v2 = 60
Therefore, v = (2*30*60)/(30 + 60) = 3600/90
v = 40

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06. Mayur left for his school at 6 am by foot and walked at the rate of 2 kmph. After reaching his school he found it was closed and immediately turned back and started walking back to his home at 3 kmph. If he reached his home at 9 am, find the distance between his school and his home.
A. 2.5 km B. 7.2 km
C. 7 km D. 3.6 km

Answer and Explanation

Answer: 3.6 km

Explanation:
Average speed of Mayur = (2*2*3)/(2 + 3) = 2.4 km/hr
If d is he distance between the school and Mayur’s home, then total distance walked by Mayur = 2d, and the total time taken is 3 hours
2.4 = 2d/3
7.2 = 2d
d = 3.6 km

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07. Two trains 140 metres and 120 metres are running in the same direction with speeds 40 kmph and 60 kmph respectively. In what time will the faster train pass the slower one?
A. 0.60 minutes B. 0.36 minutes
C. 0.78 minutes D. 0.42 minutes

Answer and Explanation

Answer: 0.78 minutes

Explanation:
Total distance = addition of length of the two trains = 140 + 120 = 260 metres
As the two trains are travelling in the same direction, their relative speed is:
v = | v1 – v2 | = | 40 – 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min
t = 260/ 1000*3
t = 0.78 minutes

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08. An athlete runs at a speed of 30 km/hr around a circular ground whose area is 2464 m2. How much time does he take to complete one round around the ground?
A. 25.25s B. 21.12s
C. 20s D. 22s

Answer and Explanation

Answer: 21.12s

Explanation:
Area of the cicular ground = 2464m2 = pr2
r = 28 m
Circumference = 2* p*r = 2*p*28 = 175.93 m = distance covered by the athlete
Speed of the athlete = 30 km/hr = 8.33 m/s
Time = distance/speed = 175.93/8.33 = 21.12s

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09. A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?
A. 14 minutes B. 12 minutes
C. 15 minutes D. 18 minutes

Answer and Explanation

Answer: 15 minutes

Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes

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10. A boats man can row in still water at speed of 7 km/hr. It takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km/hr. what is the distance between the two destinations?
A. 20 km B. 40 km
C. 30 km D. 10 km

Answer and Explanation

Answer: 40 km

Explanation:
x = 7 km/hr ; y = 3 km/hr
Ds = 10 km/hr ; Us = 4 km/hr
Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.
10*t = 4*(t + 6)
6t = 24 ; t = 4 hours
d = 10*4 = 40 km

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